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10
Inscribed Circle
Inscribed Circle
Source:
December 9, 2005
trigonometry
geometry
trapezoid
angle bisector
Problem Statement
A circle is inscribed in quadrilateral
A
B
C
D
,
ABCD,
A
BC
D
,
tangent to
A
B
‾
\overline{AB}
A
B
at
P
P
P
and to
C
D
‾
\overline{CD}
C
D
at
Q
.
Q.
Q
.
Given that
A
P
=
19
,
P
B
=
26
,
C
Q
=
37
,
AP=19, PB=26, CQ=37,
A
P
=
19
,
PB
=
26
,
CQ
=
37
,
and
Q
D
=
23
,
QD=23,
Q
D
=
23
,
find the square of the radius of the circle.
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